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Analysis of Iran Banking Sector by Multi-Layer
Approach
Ali Namaki*
*Corresponding author, Assistant Prof., Department of Finance, Faculty of
Management, University of Tehran, Tehran, Iran. (Email: [email protected])
Reza Raei
Prof., Department of Finance, Faculty of Management, University of Tehran, Tehran,
Iran. (Email: [email protected])
Nazanin Asadi
MSc., Department of Finance, Faculty of Management, University of Tehran, Tehran,
Iran. (Email: [email protected])
Ahmad Hajihasani
MSc., Department of Finance, Faculty of Management, University of Tehran, Tehran,
Iran. (Email: [email protected])
Abstract
Networks are useful tools for presenting the relationships between financial
institutions. During the previous years, many scholars have found that using
single-layer networks cannot properly characterize and explain complex systems.
The purpose of this research is to introduce a multiplex network in order to
analyze, as accurately as possible, all aspects of communication between banks in
capital market of Iran. In this article, each bank represents a node and three layers
of return, trading volume and market Cap have been presented for analyzing the
idea of multiplex networks. We have used the Granger causality method to
determine the direction between nodes. For understanding the topology structure
of these layers, different concepts have been used. The research findings show that
the value layer topology has a significant similarity with the trading volume layer.
Also according to the measure of centrality it can be seen that the centrality varies
in different layers.
Keywords: Banking Sector, Centrality, Complex System, Granger Causality,
Multiplex Network.
DOI: 10.22034/ijf.2019.101367 © Iran Finance Association
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Iranian Journal of Finance, 2019, Vol. 3, No. 1
Introduction
Network analysis is an important tool for modeling complex systems (Gaiand
Kapadia, 2010; Battiston, 2012). Researchers have been conducting various
studies by the concepts of complexity during the past years (Namaki, 2011;
Namaki, 2013). One of the most important markets that can be analyzed by
network discipline is the banking sector. In network science, the interbank
market is presented by directed and weighted graphs. Investigating the
interbank networks and understanding their systematic importance makes us
look for an appropriate analysis method.
By extension of researches on complex networks, scholars have
concluded that networks based on one type of relations cannot properly
characterize and explain complex systems (Aldasoro and Alves, 2018; Borboa,
2015).
Especially, the relation between two banks is more complex than the
information that can be summarized in one concept such as network direction
(Bargigli, 2016).
There is widespread communication between different banks, each of that
relates to a class of claims or markets (Bargigli, 2014; Bargigli, 2016).
We use multiplex networks to identify the characteristics of banks in the
capital market. Multiplex Networks (Figure 1b) are special types of Multilayer
Networks (Figure 1a) (Boccaletti, 2014). They consist of different layers and
nodes (in this research Banks) that are identical in all layers, and each layer is
based on one type of relationship (in fact each layer is a type of relationship)
(Aleta and Moreno, 2018).
Figure 1. Multilayer (a) and Multiplex (b) network
75
Analysis of Iran Banking Sector by Multi-Layer Approach
Once the layers of the capital market are formed using multiplex
networks, we will proceed to examine the topology of each layer separately.
We will use Granger causality to determine the direction and weight in each
layer (Tang, 2019; Caraiani, 2013).
Finding the characteristics of each layer, we can concentrate on important
features of the multiplex network such as centrality (Bargigli, 2016). In
networks, choosing the central or middle vertices is crucial in determining the
network topology (Shirazi, 2013). Generally, a function that assigns numeric
values to different elements in a network is called centrality.
There are different centrality measurers for evaluating network elements,
some of them are defined on vertices and others on network edges (Zheng,
2012; Junker and Schreiber, 2008). Generally, the centrality of a node in a
network is a criterion of node importance (Bargigli, 2016). In this study,
centralities are devoted to the evaluation of network nodes. Node centrality is
essential for identifying the most important nodes in any network architecture.
The three most commonly used methods for measuring centralities are degree
Centrality, Betweenness Centrality, and Eigenvector Centrality, which have all
been calculated in this paper. Identification of central banks in the different
layers and the whole layer is one of the essential achievements of this study.
These banks are the source of contagion in financial markets. So, in order to
prevent a financial contagion, it is important to identify these central banks
(Kermarrec, 2011; Yu and Fan, 2015).
Until now, most researches in the complexity science are based on the
analysis of single-layer networks. Multilayer networks have not been widely
used in the economy discipline. Also, domestic market studies have not
analyzed the financial markets using multiple networks. Bargigli et.al have
investigated the structure of the Italian interbank market using multiplex
network approach. They have analyzed the financial networks based on two
different layers of maturity and the type of contract (Bargigli, 2014). Molina
et.al has studied the relationship between Mexican banks through the
multilayer network approach (Borboa, 2015). Eldaroso et.al have considered
large European banks by maturity and instrument type to describe the main
features of a multiplex network (Aldasoro and Alves, 2018). Using different
types of interbank exposures, Cont et.al have investigated the systemic risk in
the Brazilian market and the potential contagion contamination (Cont, Moussa
and Santos, 2010). In this research seventeen listed banks of Tehran Stock
Exchange have been analyzed from March 2016 to March 2019. The three
listed banks, Sarmayeh, Iran Zamin and Qarz-al-Hasaneh Resalat were not
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Iranian Journal of Finance, 2019, Vol. 3, No. 1
considered due to the low trading days. This research organized in 4 sections.
In part 2 the statistical models and methods will be defined. Data analysis and
implementation of statistical models are considered in section 3. Section 4 has
been dedicated to conclusions.
Methods
1. Detrending Data
In order to eliminate potential trends from daily trading volumes and trading
value data, we use regression on a quadratic function of time. The quadratic
function includes linear and nonlinear time trends in data (Andrew and Wang,
2000, Chen, Firth and Rui, 2001)
Here is the raw data and denotes the residuals.
2. Hsiao Granger Causality Test
Granger (1969) proposed an idea to better and more accurately estimate
variables based on their relationships with their past quantities. The main
drawback of the standard Granger Causality Test is the sensitivity to the choice
of interrupt length, so that different interrupt lengths will, in most cases, yield
different results. Therefore, Hsiao (1981) proposed a systematic self-
explanation method for solving this problem to select the optimal interval
length for each variable.
The selection of the optimal interrupt length is performed in two stages
using the Hsiao Granger causality test method. In the first step, a set of self-
explanatory regressions on the dependent variable is estimated. In the
regression equations of this step, the dependent variable starts from one lag,
and then subsequently another lag is added to each regression. It is advisable to
add as many lags as possible. Estimated regressions will be as follows:
∑
After estimating all regressions, the final prediction error (FPE) criterion
for each regression equation is calculated based on the following relation:
In this formula T is the sample size and ESS is the sum of squares of the
residuals.
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Analysis of Iran Banking Sector by Multi-Layer Approach
The interval that meets the minimum FPE criterion will be the optimal
interval length (m*). By setting m*, the first step of the test is completed. In the
second step, the other variables with lags are entered into the regression
equations. These regression equations are defined as:
∑ ∑
Then the final prediction error criterion for each regression equation is
calculated by the following method:
The interval length that minimizes the final predictive error criterion
(FPE) is the optimal interval length X. In the Hsiao Granger Causality Test,
FPE (m*) is compared with FPE (m*, n*). If FPE (m*, n*)>FPE (m*), is
not the cause of , and if FPE (m*, n*) is <FPE (m*), is the cause of . In
the Hsiao Granger Causality Test, all variables are required to be stationary and
if the variables are non-stationary, their first stationary difference must be used
to perform the test.
3. Topology measures
3.1. Strength
The strength of a node is as follows:
∑
𝛹
Where 𝛹 is the neighborhood set of node i. we consider ( )
as the strength of edge (i, j).
3.2. Reciprocity
In direct networks, such as interbank networks, it is appealing to measure the
likelihood of occurring double edges with opposite directions between two
specific nodes. For calculating the reciprocity, there are different methods
(Newman, 2002) .One of the reference formula for calculating the reciprocity
is based on the correlation coefficient between matrix A and AT, and the
equation is as follows (Soramaki, 2007):
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Iranian Journal of Finance, 2019, Vol. 3, No. 1
𝜌 ∑ ( )( )
∑ ( )
is the average value of inputs A.
3.3. Density
The simplest measure for directed graphs is density. This is the ratio of the
number of edges in the network to the number of possible edges representing
the network density index and always between zero and one. This measure is
defined as follows:
Where n = |V|, l = |E|, V is the vertex or node set and E is the edge or link
set (Bargigli, 2014).
3.4. Clustering coefficient
The clustering coefficient indicates how closely the vertices around the target
node are interconnected, and measures the probability that the node or vertices
belong to a specific cluster. The directed clustering coefficient of network node
is defined as follows (Fagiolo, 2007):
∑ ( ) ( )
In the above formula, is the sum of the node degrees , which means
that
and ∑ are the number of bidirectional edges.
4. Similarity measures
The cosine coefficient is most commonly used to measure the similarity of
vectors. The cosine similarity is defined as follows:
‖ ‖‖ ‖
∑
√∑
√∑
This coefficient is set to the interval of [-1, 1] (if the vectors are
nonnegative this value will be in the interval [0, 1]. Here is the angle between
p and q.
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Analysis of Iran Banking Sector by Multi-Layer Approach
5. Measures of centrality
5.1. Degree centrality
One of the widely used centrality measures is the degree of centrality
(Landherr, Friedl and Heidemann, 2010). The centrality of the node’s degree is
equal to the number of edges on that vertex. Suppose that G = (V, E) is an
undirected graph with |V| as Vertex and |E| as Edge. Also, e = {v, u} denotes
the undirected edge in graph G. The degree centrality of that node is defined as
follows:
|{ | { }}|
In a directional network, there are usually two measures for the
calculation of degree centrality based on the input and output conditions. If e =
(v, u) denotes the direction of the vertex from to then we have:
|{ | }|
|{ | }|
5.2. Betweenness centrality
The measure of intermediate centrality specifies the number of times a node
acts as a connection through the shortest path between two nodes. is the
most appropriate centrality measure to determine the importance of a node and
its effect on the overall graph connection (Kermarrec, 2011).
∑
Where is the shortest number of paths from node to node in the
network, is the number of shortest paths through nodes . is one of
the standard measures for node centrality, which was originally introduced to
determine the importance of a node in a network (Boldi and Vigna, 2014). The
higher the betweenness centrality of a vertex is the more the effect of that node
on the system (Faghani and Nguyen, 2013; Liu, 2015).
5.3. Eigenvector centrality
Another centrality introduced by Bonacich (2007) is called eigenvector
centricity. The basic idea of the eigenvector centrality is that the importance of
a node is not only determined by itself but also influenced by the importance of
its neighbors (Yu and Fun, 2015). In other words, by this measure the centrality
of each vertex is directly related to the centrality of the adjacent vertices. So
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Iranian Journal of Finance, 2019, Vol. 3, No. 1
the higher centrality value of the neighbors of a node leads to higher centrality
of that node. If corresponds to the largest eigenvalue of matrix A, in other
words,
‖ ‖
Then the eigenvector centrality of vertex at { } is equal
to the element of the corresponding eigenvector of (Landherr, Friedl and
Heidemann, 2010; Kermarrec, 2011).
Data Analysis and Finding Results
In this section, we form a graph corresponding to each of the network layers
including the layers of return, trading volume, and the value. The network
corresponding to each layer is a weighted and directed graph. For this purpose
and to determine the direction of the edges in each of the graphs, Granger
causality test was applied and the weight of the edges was assigned based on
the final prediction error (FPE). Charts 2, 3, and 4 represent the graph
corresponding to the layers of return, volume and value, respectively.
Figure 2. Graph corresponding to return layer
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Analysis of Iran Banking Sector by Multi-Layer Approach
Figure 3. Graph corresponding to volume layer
Figure 4. Graph corresponding to value layer
1. Network layer topology
In order to evaluate different layers of the network, we have computed some
network metrics including density, reciprocity, node strength, and node
clustering coefficients. We have examined all of these measures in each layer
of the network. Table 1 shows the density and reciprocity in each layer of the
network.
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Iranian Journal of Finance, 2019, Vol. 3, No. 1
Table 1. Density and reciprocity measures in different network layers
Return layer Volume layer Value layer
Reciprocity 0.369527 0.0482 0.094504
Density 0.430147 0.474265 0.525735
Figures 5 illustrates the strength of the various nodes of the network in
different layers.
Figure 5. The strength of the nodes in the different layer
83
Analysis of Iran Banking Sector by Multi-Layer Approach
In Figures 6, the clustering coefficients of different network nodes in the
layers of returns, trading volume and transaction value are presented.
Figure 6.Clustering coefficients of nodes in different layer
2. Similarity of network layers
In this section, the similarity of the market value layer as a total layer to each
of the returns and volume layers is investigated. For this purpose, the cosine
similarity coefficient has been applied using the node strength vector and node
clustering coefficients vector for different layers. The values obtained for the
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Iranian Journal of Finance, 2019, Vol. 3, No. 1
cosine similarity coefficient are presented in Table 2. Based on the values
obtained, it is obvious that the market value layer is almost the same as the
trading volume layer.
Table 2. Similarity of different layers to the value layer
Cosin similarity (strength) Cosin similarity (D. C. C.)
Similarity between value and return layer %3.32 %-81.82
Similarity between value and volume layer %94.22 %96.58
3. Centrality in network layers
In this section, the centrality of nodes in each layer is evaluated using degree,
betweenness, and eigenvector centrality. Based on these measures the importance of
the banks in each layer and how they behave in different layers has been evaluated.
Tables 3, 4 and 5 show the centrality of each bank in terms of different layers. Also
the rank of each bank is calculated according to the measures.
Table 3. Degree centrality in each layer
Bank
Return layer Trading Volume layer Value layer
Measure Rank Measure rank measure Rank
E.N. 18 5 18 8 22 1
Ansar 4 17 6 15 5 16
Ayandeh 17 6 3 16 7 15
Parsian 27 1 21 3 23 3
Pasargad 8 12 10 13 12 12
Tejarat 18 4 20 4 21 7
Hekmat 7 14 3 17 4 17
M.E. 15 8 16 10 17 11
Day 15 7 20 5 22 5
Saman 14 9 27 1 27 1
Sina 25 2 20 6 22 6
City 5 15 12 12 12 13
Saderat 13 11 15 11 19 9
Ghavamin 4 16 9 14 10 14
Karafarin 7 13 17 9 18 10
Mellat 13 10 22 2 25 2
Post Bank 24 3 19 7 20 8
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Analysis of Iran Banking Sector by Multi-Layer Approach
Table 4. Betweenness centrality in each layer
Bank
Return layer Volume layer Value layer
Measure Rank measure rank measure Rank
E.N. 17 3 0 17 0 17
Ansar 0 17 14 6 3 10
Ayandeh 7 9 1 11 15 7
Parsian 3 11 0 16 0 16
Pasargad 15 6 28 4 17 5
Tejarat 11 8 46 1 25 3
Hekmat 0 16 26 5 0 15
M.E. 0 15 38 2 15 6
Day 15 5 0 15 0 14
Saman 5 10 13 7 27 2
Sina 16 4 0 14 24 4
City 0 14 12 9 11 9
Saderat 14 7 8 10 0 13
Ghavamin 0 13 0 13 0 12
Karafarin 0 12 12 8 12 8
Mellat 19 2 34 3 45 1
Post Bank 46 1 0 12 0 11
Table 5. Eigen vector centrality in each layer
Bank Return layer Volume layer Value layer
Measure Rank measure Rank measure Rank
E.N. -0.2885 13 0.0404 10 0.0400 10
Ansar -0.0043 2 0 15 0.0001 16
Ayandeh -0.2801 12 0 16 0.0070 14
Parsian -0.2251 8 0.0791 7 0.0579 9
Pasargad -0.0796 6 0.1845 4 0.2825 4
Tejarat -0.2744 11 0.6702 1 0.5017 2
Hekmat -0.0468 5 0.0006 14 0.0000 17
M.E. -0.2141 7 0.0493 9 0.0654 8
Day -0.3236 15 0.1535 5 0.1259 6
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Iranian Journal of Finance, 2019, Vol. 3, No. 1
Saman -0.4308 17 0.0326 11 0.0376 12
Sina -0.3101 14 0.1411 6 0.1280 5
City 0 1 0.016 13 0.0099 13
Saderat -0.2329 9 0.3725 3 0.2879 3
Ghavamin -0.0258 3 0 17 0.0003 15
Karafarin -0.0335 4 0.0314 12 0.0379 11
Mellat -0.2612 10 0.5631 2 0.7305 1
Post Bank -0.3838 16 0.0699 8 0.0868 7
Conclusion
Multilayer network concept is the expansion of the network theory that can be
used for better understanding the behavior of real markets.
In this paper, we have used this new concept to analyze the relationships
between banks in Iranian capital market for three consecutive years. We have
presented a three-layer network, with each layer corresponding to a specific
network. The multiplex network is composed of the daily returns, trading
volume and market values (named as the global layer) of the banking sector.
To investigate the topology of different layers of the network, we have
used various measures, such as graph density, reciprocity, node strength, and
clustering coefficients.
It is found that each layer has unique topological features, but the
estimated densities of these layers are the same. The calculated reciprocity
indicates that the difference between trading volume and value layers is less
than the difference between the return and value layers in the terms of the
corresponding graph edges.
After observing the strength values of the nodes in different layers of the
network, we have found that the global layer (value layer) is very similar to the
trading volume layer. The same result can be obtained by examining the values
of clustering coefficients of nodes in different layers. To investigate the
similarity of the global layer with the return and trading volume layers, the
cosine similarity coefficient has been used. We have calculated this measure
once by using the node strength vector and again by using the node clustering
coefficients vector in different layers. The value of this coefficient in the case
of the nodes strength indicates the high similarity of the global layer to the
trading volume layer. This finding has been confirmed by using clustering
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Analysis of Iran Banking Sector by Multi-Layer Approach
coefficients. Finally, we have tried to define central nodes of the layers. For
this purpose, we have used the measure of degree centrality, betweenness and
eigenvector centrality. It is shown that there is a significant relationship
between centrality of each bank in different layers.
Some medium-sized banks are central in some layers and peripheral in the
other layers. Large banks such as Mellat Bank are in the core of all layers by
different measures.This approach is useful for the policy makers to estimate the
systemic risk and contagion in the financial sector.
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Bibliographic information of this paper for citing:
Namaki, Ali; Asadi, Nazanin; Hajihasani, Ahmad & Raei, Reza (2019). Analysis of
Iran Banking Sector by Multi-Layer Approach. Iranian Journal of Finance, 3(1), 73-
89.
Copyright © 2019, Ali Namaki, Nazanin Asadi, Ahmad Hajihasani and Reza Raei